1. Approaches to quantifying uncertainty-related risk There are three approaches to dealing with financial and economic risk in benefit-cost analysis: = expected values (certainty equivalents) of scenarios; = risk-adjusted discount rates; and = risk analysis through simulation. Given the present state of the art, the first two approaches have limited applicability. Only the third method, simulation, offers a practical technology for analyzing the overall risk of a project.

2. Expected values of scenarios If an investment has two possible outcomes - $10 and $100- and their probabilities are 30 and 70 per cent, respectively, then the expected value or certainty equivalent of the investment is (0.3 x $10) + (0.7 x $100) = $3 + $70 = $73. If you have a completely rational attitude to risk, then it shouldn’t matter to you whether you make the investment or accept the $73 instead.

3. Example: Few benefit-cost analysts take this scenario approach because in most cases there are so many possible outcomes that it is too difficult to think clearly about the probability of each separately. On occasion, however, scenarios can provide useful information about risk. For example, an oil company is trying to decide whether to build a new pipeline across an iceberg-infested strait. The pipeline costs $100 million (present value at t0). The chief executive officer (CEO) foresees three possible scenarios; and each of these has a predictable outcome for the company.

4. Scenario 1: No iceberg hits the pipe. Outcome: Company revenue from the pipeline: $135 million, t0. Scenario 2: An iceberg hits the pipe, but the pipe can be repaired. Outcome: Company revenue from the pipeline: $93 million, t0. Scenario 3: An iceberg hits the pipe, and the pipe cannot be repaired. Outcome: Company revenue from the pipeline: $9 million, t0.

5. Now comes the difficult part. Suppose the CEO commissions a study by iceberg-risk consultants and is told that there is a 60 per cent chance that no iceberg will hit the pipe, a 30 per cent chance that an iceberg will hit the pipe but the pipe will be repairable, and a 10 per cent chance that an iceberg will hit the pipe and the pipe will not be repairable. Therefore, the expected value of the $100 million investment is (0.6 x $135 million) + (0.3 x $93 million) + (0.1 x $9 million) = ($81 + $27.9 + $0.9 million) = $109.8 million. The CEO decides to go ahead with the pipeline. since the expected benefit ($109.8 million) is greater than the cost ($100 million). An iceberg hits the pipe, but the pipe is reparable. The company loses $7 million. The CEO, however, had made the right decision, given the information he or she had to work with.

6. Risk-adjusted discount rates Another approach that purports to deal analytically with risk is risk-adjusted discount rates. The basic idea is that, in a perfect market, all investments earn the same rate of return. Otherwise, capital would flow to the high-return areas pushing average returns down until the rates equalised. Therefore, visibly different rates of return must incorporate the same basic rate plus a premium for risk so that, in the long run, only the basic return is gathered by the investor. If this is so, then the appropriate discount rate (cost of capital) is the basic rate plus a premium for risk. This combination is the risk-adjusted discount rate.

7. Simulation Model A simulation model is a mathematical model that calculates the impact of uncertain inputs and decisions we make on outcomes that we care about, such as profit and loss, investment returns, etc. A simulation model will include: – Model inputs that are uncertain numbers/ uncertain variables – Intermediate calculations as required – Model outputs that depend on the inputs -- These are uncertain functions

8. Simulation techniques Simulation techniques can be used to assist management decision-making, where analytical methods are either not available or inappropriate. Typical business problems where simulation could be used to aid management decision-making are – Inventory control. – Queuing problems. – Production planning.

9. Risk analysis through simulation Simulation predicts the possible outcomes of the benefit-cost model, given the variables that influence those outcomes. It enables the analyst to give more comprehensive and realistic advice to the decision-maker. In the older deterministic method of benefit cost analysis, the analyst offered a single figure for NPV, but it was always unclear what the probability of this single outcome was. The decision-maker did not know how much confidence to place in the figure and therefore tended to make a subjective judgement.

10. Simulation shows the range of NPVs possible, given the factors that can vary, and provides an overview of the probabilities within that range. Decision-makers know there is risk in every decision. There are no guarantees. Sometimes the right decision doesn’t turn out well because the changeable factors turn unfavourable. The decision maker relies on the analyst to give as full and accurate a picture of the possible risks and rewards as possible.

11. The main difference between this procedure and the recommended simulation procedure is in the reliability of the estimates of probability they make. Did the iceberg-risk consultants really have the expertise to assign probabilities to the likelihood of an iceberg collision? There were no data. Assigning subjective probabilities to ‘big-picture’ scenarios is essentially a guessing game. In contrast, it is plausible that an apple-pricing expert can forecast apple prices within a reasonable range a year ahead, based on historical price data, demand trends, and consideration of factors that might intrude. There is a subjective or judgmental element in forecasting apple prices, too, but there are data available. Legitimate experts have developed good judgement in the matter, so they are able to express expected apple prices as a range and specify a probability distribution with reasonable confidence. Risk analysis is part science and part art; and part of the art is knowing when and where in the benefit-cost model to use probabilistic data.